On the Convolution Theorem of the Mehler‐Fock‐Transform for a Class of Generalized Functions (I)

Abstract

Synopsisusing results of BUGGLE and TIWARI, PANDEY on the AlEHLER-FOCK-transforin in certain spaces of generalizcd functions we introduce a convolution structure for these spaces, such that a convolution theorem of the ~IEHLER-FocH-transform can he proved.

Electric forces induced by a charged colloid particle attached to the water–nonpolar fluid interface

“…The Mehler-Fock transform [32][33][34][35][36][37][38], and the generalized Mehler-Fock transform [38,[43][44][45] have found applications for solving various problems of similar geometry [42,46,47]. In view of Eq.…”

Characterization of Weyl operator in terms of Mehler–Fock transform

“…Translation operator is one of the fundamental operators in time‐frequency analysis. The generalized translation or shift operator corresponding to Mehler–Fock transform for is defined as 19 where with It is evident that K ( x , y , z )= K ( y , x , z )= K ( x , z , y ), and …”

On the convolution theorem of the finite Legendre transform in a Zemanian space

“…As the next step, we shall see that last expression defines a function H(x) = (g(y),TMy)) (3.5) which belongs to A (-1,1). And we achieve this objective with the aid of the procedure employed by H. J. Glaeske and A. Hess in [5] and [6] with regard to the Mehler-Fock transform.…”

“…(3)(4)(5)(6) For it, we fix arbitrarily χ in -1 < χ < 1. Notice that the successive derivatives of the translation operator are ir,,,/ χ^ψ…”